1. Dual-Channel FFT Analysis: A Presentation Prepared for Syn-Aud-Con: Test and Measurement Seminars Louisville, KY Aug. 28-30, 2002

2. Presenter Jamie Anderson –SIA Product Manager –Jamie@SIASoft.comJamie@SIASoft.com SIA Software Company, Inc One Main Street Whitinsville, MA 01588 508.234.9877 www.siasoft.com

3. Fast Fourier Transforms “Our Friend the FFT”

4. The Fourier Transform Jean Baptiste Joseph Fourier –All complex waves are composed of a combination of simple sine waves of varying amplitudes and frequencies Amp vs Time to Amp vs Freq Waveform to Spectrum

5. Transforms A transform converts our data from one domain (view) to another. –Same data Is reversible via Inverse Transform –Unlike a conventional RTA using a bank of analog filters, FFT’s yield complex data: Magnitude and Phase information Amp vs Time to Amp vs Freq Waveform Spectrum Time Domain to Frequency Domain

6. FFT Resolution Reciprocal Bandwidth: FR=1/TC Frequency Resolution = 1/Time Constant –Larger Time Window: Higher Resolution Slower (Longer time window and more data to crunch) –Smaller Time Window: Lower Resolution Faster Time Constant = Sample Rate x FFT Length * Decimation – Varying SR & FFT to get constant res.*

7. FFT Parameters: Time Constant (TC) vs. Frequency Resolution (FR) Linear Frequency Scale TC = FFT/SR FR = 1/TC

8. FFT Resolution FFT’s yield linear data –Constant bandwidth instead of constant Q –FFT data must be “banded” to yield fractional- octave data. FFT must be windowed –FFT’s assume data is continuous & repeating so wave form must begin and end at 0. –Windows are amplitude functions on data

9. FFT Parameters: Time Constant (TC) vs. Frequency Resolution (FR) Log Frequency Scale

10. Linear vs. Log Banding Linear banding has an increasing number of bands per octave as frequency increases, resulting in less energy per band in the HF. Pink Noise (equal energy per octave) shown w/ linear and log banding. Fractional–octave (log) banding has an equal number of bands per octave, resulting in equal energy per band.

11. FFT Data Windows An FFT assumes that a waveform that it has sampled (defined by its time window) is infinite and repeating. So if the waveform does not begin and end at the same value, the waveform will effectively be “distorted”.

12. FFT Data Windows FFT data windows force the sampled waveform to zero at the beginning and end of the time record, thereby reducing the impact of the “Infinite and Repeating” assumption. Each data window has a corresponding spectral distribution (analogous to filter shape.) The FFT data window being used and its corresponding distribution must be taken into consideration when banding the resulting spectral data into fractional- octave bands.

13. Dual-Channel Measurement

14. Systems InputOutputSystem Note: These systems can be anything from a single piece of wire to a multi-channel sound system with electrical, acoustic and electro- acoustic elements, as well as wired and wireless connections. And remember, it only takes one bad cable to turn a $1,000,000 sound system into an AM radio!

15. Measurement Types Analyzers are our tools for finding problems Different measurements are good for finding different problems

16. Measurement Types: Single Channel vs. Dual Channel Single Channel: Absolute Dual Channel: Relative - In vs Out A(  )B(  )H(  ) Frequency Response H(  ) = B(  )/A(  ) Input Signal = A (  ) Output Signal = B(  )

17. Measurement Types: Single Channel SPL & VU Wave Form –Amplitude vs. Time Spectrum –Amplitude vs. Frequency

18. Measurement Types: Dual Channel Transfer Function: Frequency Response –Phase vs. Frequency –Magnitude vs Frequency Impulse Response –Magnitude vs Time –“Echo structure”

19. Transfer Function Measurement Channel (RTA) Reference Channel (RTA) Transfer Function System Input Signal Output Signal

20. Transfer Function Measurement Channel (RTA) Reference Channel (RTA) Transfer Function System Input Signal Output Signal

21. Transfer Function Measurement Channel (RTA) Reference Channel (RTA) Transfer Function System Input Signal Output Signal

22. What do you get if you transform a transfer function? IFT produces impulse response Transfer Function... To... Impulse Response *So... If Frequency Response can be measured source independently - so can Impulse Response*

23. Dual-Channel FFT Issues Window Length vs Resolution FR = 1/TC Source Independence Propagation Time Linearity Noise –Averaging –Coherence System Input Signal Output Signal

24. How Dual-Channel FFT Analyzers Work System Input Output Wave Measurement Signal Reference Signal

25. System Input Output FFT RTA = Wave Spectrograph RTA How Dual-Channel FFT Analyzers Work

26. System = Input Output FFT Transfer Function (Frequency Resp.) RTA Wave How Dual-Channel FFT Analyzers Work

27. System = Input Output FFT IFT Transfer Function (Frequency Resp.) RTA Impulse Resp. Wave How Dual-Channel FFT Analyzers Work

28. Basic Measurement Set-up SourceEQ / ProcessorAmplifier Loudspeaker & Room Microphone Computer w/ Stereo line-level input Mixer

29. Basic Measurement Set-up SourceEQ / ProcessorAmplifier Loudspeaker & Room Microphone Computer w/ Stereo line-level input Mixer Control Data EQ/Processor Control

31. Any idiot can get squiggly line to appear on an analyzer screen. Our goal is to make ones we can make decisions on. Remember: Computers do what we tell them to do, not what we want them to do.

32. To use an analyzer, we must first: 1.Verify that we are making our measurements properly. 2.Verify that it is an appropriate measurement for our purpose.

33. An analyzer is only a tool: YOU make the decisions You decide what to measure. You decide which measurements to use. You decide what the resulting data means. And you decide what to do about it.

34. Our goal is to fix our system not the trace on the screen.

35. Decimation